Wow! Just wow! I feel sorry for your gf (even if she does sound screwed in the head)
How to cheat without getting caught...
1) set up a habit of going out with the guys regularly. Make these nights out all nighters. Do not cheat in the set up phase of this routine.
2) Once she is comfortable with these guys nights out and she has accused you of cheating when you haven't been and you've been able to honestly deny it, start finding some skank to flirt with
3) start f**king said skank
In all of this you have to make sure that you are out with mates that dislike your gf enough to not want to tell her the truth.
So there's how to do it. Yes it makes you an arsehole to want to do this. You wanna know something, you will actually feel like an arsehole when your relationship goes down the crapper for some other reason. You will feel like shit, no matter how well you can justify it now you will have to live the rest of your life knowing you are a deceitful prick and if you have a modicum of decency you will spend the rest of your life trying to become a better person.
(and before anyone asks, yes I know all this through personal experience. I cheated on my ex and had a huge amount of 'justification' at the time. I not only did it once, but 3 times. He never found out, still doesn't know. I have to live with myself now. Hubby knows I cheated on my ex, I thought it only fair he knows. I came close to cyber-cheating on hubby when our son was a sickly infant but instead I told him how I was feeling and worked things out with him. I couldn't do that to him and I am so proud of myself for making the right decision in this relationship. Because I discussed that urge with him, I'm over it. I don't even entertain the thought of women anymore because that feels like cheating too.... shit. where was I? Oh yeah, I can tell you from personal experience that not only are you an arsehole, you will agree with everyone who thinks that of you if you go through with cheating on your gf. Break up with her FFS.)
'People are never perfect but love can be. People waste time looking for the perfect lover rather than creating the perfect love' - Princess Leigh-Cheri from Still Life With Woodpecker.